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Numbers in the 5-cycle-attractor of the function f(x)=A063919(x).
24

%I #22 Jan 25 2024 08:01:26

%S 1482,1878,1890,2142,2178

%N Numbers in the 5-cycle-attractor of the function f(x)=A063919(x).

%C A002827 provides 1-cycle terms = unitary perfect numbers.

%C A063991 gives 2-cycle elements = unitary amicable numbers.

%C A097030 collects true 14-cycle elements, i.e., terms in end-cycle of length 14 when A063919(x) function is iterated.

%C Concerning 3-cycle elements, only {30,42,54} were encountered.

%H J. O. M. Pedersen, <a href="/A097024/a097024.txt">Order 5 cycles</a>, 2007.

%t a063919[1] = 1; (* function a[] in A063919 by _Jean-François Alcover_ *)

%t a063919[n_] := Total[Select[Divisors[n], GCD[#, n/#]==1&]]-n/;n>1

%t a097024Q[k_] := Module[{a=NestList[a063919, k, 5]}, Count[a, k]==2&&Last[a]==k]

%t a097024[n_] := Select[Range[n], a097024Q]

%t a097024[2178] (* _Hartmut F. W. Hoft_, Jan 24 2024 *)

%o (PARI) f(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) - n;

%o isok5(n) = iferr(f(f(f(f(f(n))))) == n, E, 0);

%o isok1(n) = iferr(f(n) == n, E, 0);

%o isok(n) = !isok1(n) && isok5(n); \\ _Michel Marcus_, Sep 28 2018

%Y Cf. A063919, A002827, A063991, A097030.

%K nonn,more

%O 1,1

%A _Labos Elemer_, Aug 30 2004